%I A147833
%S A147833 1,0,0,12,12,60,252,636,2364,7932,25020,85116,280380,921084,3063996,
%T A147833 10112892,33421884,110641404,365683644,1209311868,3999743292,
%U A147833 13225194492,43735910076,144633607548,478279581756,1581644932860
%N A147833 A vector matrix Markov based on the simplex point matrix for the {3.4,
               5} triangle:Points{x,y}:{0,0},{0,3},{0,4}; M0={{1,0,0} {1,0,3}, {1,
               4,0}}; 3^2+4^2=5^2; with characteristic polynomial: 12 + 4 x + x^2 
               - x^3
%C A147833 This area one simplex matrix when rotated {{1,0,0} {1,0,1}, {1,1,0}} 
               Gives: {{0,1,0}, {0,0,1}, {1,1,1}} which is associated with the tribonacci 
               or Rauzy tile. That open the way for the 3,4,5 triangle being: {{1,
               0,0} {1,0,3}, {1,4,0}} 3^2+4^2=5^2 The Markov matrix is then: {{0,
               3,0}, {0,0,4}, {1,1,1}} Equivalent matrix in standard form is: {{0, 
               1, 0}, {0, 0, 1}, {12, 4, 1}}
%F A147833 M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}}; v(n)=M^n.v(0);v(0)={1,0,0}; a(n)=v(n)[[1]].
%t A147833 Clear[M, v, f, g, x, n] M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}} v[0] = 
               {1, 0, 0} v[n_] := v[n] = M.v[n - 1] Table[v[n][[1]], {n, 0, 30}]
%Y A147833 Sequence in context: A070710 A048759 A119877 this_sequence A003877 A161196 
               A111306
%Y A147833 Adjacent sequences: A147830 A147831 A147832 this_sequence A147834 A147835 
               A147836
%K A147833 nonn
%O A147833 0,4
%A A147833 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Nov 
               14 2008